Deriving State Block Diagrams That Correctly Model Hand-Code Implementation—Correcting the Enhanced Luenberger Style Motion Observer as an Example

This article presents a detailed analysis of the enhanced Luenberger style motion observer (ELSO) for motor control applications. The analysis reveals that the state block diagram presented in the literature does not correctly represent the hand-code implementation of the structure that is presented in that same literature. As a result, the block diagram does not correctly model ELSO dynamic behavior. Here, a discussion of some common errors in discrete observer modeling is presented and used to correct the ELSO state block diagram. These common errors include: first, failing to model the inherent delay present in the feedback path of all discrete state-filter and observer structures, second, incorrectly modeling the difference equation index shifts that exist in nearly all observer structures, and third, improper signal nomenclature for the observer predicted states. In this article, the ELSO block diagram and code implementation from the literature is reviewed and the modeling errors are exposed. Finally, correction of these modeling errors is presented. The discrete modeling techniques presented in this article are applicable to all discrete state filters and observers.